GroupTheory`
GroupTheory`
GTTbSpinOrbit
GTTbSpinOrbit[hamiltonian,spin-orbit interaction]
adds spin-orbit coupling to a given tight-binding Hamiltonian due to a specified spin-orbit interaction.
Details and Options
- A Hamiltonian with spin-orbit coupling (SOC) is constructed in two steps. First, the Hamiltonian without SOC is needed, and second GTTbSpinOrbit can be used to add SOC.
- The spin-orbit interaction is specified by a vector of the following form:
- spin-orbit interaction = {atom1,atom2,...};
atom1={bdim,l,pos,ξ} - The dimension of the block corresponding to atom1 in the Hamiltonian hamiltonian is given by bdim. The position of the block with angular momentum l for inclusion of SOC is determined by pos. ξ is the strength of SOC.
- The Hamiltonian without SOC can be calculated using GTTbHamiltonian.
- The following option canb e used:
-
GOVerbose False Controls the output of additional information - See: W. Hergert, M. Geilhufe, Group Theory in Solid State Physics and Photonics. Problem Solving with Mathematica
Examples
Basic Examples (1)
The Hamiltonian for the fcc structure is already constructed and will be read from file:
We assume that the Hamiltonian for Au will be constructed. At first, the structure of the standard fcc-Hamiltonian is shown.
The fcc Hamiltonian will be doubled. It represents the up and down spin directions without SOC.
The SOC will be introduced for the d electrons.
The difference of the two Hamiltonians demonstrates, which matrix elements mediate the SOC.